In this respect, a
widely studied simplest modification of \(\mathrm {GR}\)  is the
\(f(\mathbf {R})\)  gravity
[1]}, [2]}, where
\(\mathbf {L}_{GR}=\mathbf {R}\)  is replaced by a generic function of
\(\mathbf {R}\) , i.e., \(\mathbf {L}_{f(\mathbf {R})}=f(\mathbf {R})\) . We
may explore the non-linear effects emerging from the curvature
scalar \(\mathbf {R}\)  in the cosmic evolution by making a suitable
choice of the generic function \(f(\mathbf {R})\) , using this
modification of \(\mathrm {GR}\)  [3]}, [4]}.
Amendola et al. [5]} formulated some particular
conditions for the viability of \(f(\textbf {R})\)  \(\mathrm {DE}\)  models
and investigated the stability of these models to understand the
cosmic evolution. Capozziello et al.
[6]} discussed certain key aspects of
\(f(\mathbf {R})\)  cosmology and found this extension of \(\mathrm {GR}\) 
to be very promising to retrace the late-time cosmology to the
inflationary epoch. Nojiri and Odintsov [7]}
proposed a generic formulation of \(f(\mathbf {R})\)  model of DE which
may be reconstructed via a particular \(\mathrm {FLRW}\)  spacetime.
They explored some realistic form of \(f(\mathbf {R})\)  models
describing different cosmic phases.
